%!TEX program = xelatex
\documentclass[10pt,UTF8]{ctexbook}
\usepackage{ctex}
\usepackage{fontspec}
\setmainfont{CMU Serif}

%B5
%\usepackage[papersize={185mm,230mm},body={155mm,190mm},left=15mm,top=10mm,includeheadfoot, head=15pt]{geometry}


%A5
\usepackage[papersize={148mm,210mm},body={122.6mm,164.6mm},left=12.7mm,top=12.7mm,includeheadfoot, head=15pt]{geometry}



\setlength{\parindent}{2em}
\setlength{\parskip}{3pt plus1pt minus2pt}
\ctexset{%
	contentsname={目\ \ 次},
	listfigurename={插\ 图\ 目\ 录},
	listtablename={表\ 格\ 目\ 录},
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		titleformat={\large\bfseries}
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		nameformat={\bfseries},
		titleformat={\bfseries}
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}
%%===== 中英文字体
%\setmainfont{Adobe Garamond Pro} %{Minion Pro} % 衬线字体 roman \rmfamily
%\setsansfont{Myriad Pro} % 无衬线字体 sans serif \sffamily
%\setmonofont{Consolas}   % 等宽字体 typewriter \ttfamily
%% 中文字体
%\setCJKmainfont[BoldFont={方正小标宋_GBK},%FZHeiGB18030,FZSongHeiGB18030}, %
%                ItalicFont={FZBeiWeiKaiShuS}]%FZKaiGB18030
% {FZShuSongGB18030}%{FZBoYaSong,NSimSun,Adobe Song Std L}
%\setCJKsansfont{FZHeiGB18030}
%\setCJKmonofont{FZKaiGB18030}
\newcommand{\song}{\songti}
\newcommand{\hei}{\heiti}
\newcommand{\kai}{\kaishu}
%\setCJKfamilyfont{BWKai}{FZBeiWeiKaiShuS}\newcommand{\BWKai}{\CJKfamily{BWKai}}
\newcommand{\BWKai}{\kai}

\newcommand*\norm[1]{\|#1\|}
\newcommand*\abs[1]{\lvert#1\rvert}
%===== 常用宏包
\usepackage{amsmath,amssymb,amsfonts,bm}
\usepackage{esint}
\usepackage{extarrows}
\usepackage{fancyhdr}  % 页眉和页脚
\usepackage{listings}  % 源代码
\usepackage{makeidx}\makeindex   % 索引
\usepackage{graphicx,xcolor}\graphicspath{{figures/}}
\usepackage{subfigure} % 子插图
%\usepackage{picins} % 图文混排, texlive 不支持
%\piccaption{This is caption\label{aaa}}
%\parpic[r]{\includegraphics[width=5cm]{aaa.jpg}}
%\usepackage{picinpar}
%\begin{figwindow}
%\usepackage{epstopdf} % 处理 eps 图片
\usepackage{tikz}
\usetikzlibrary{arrows,backgrounds,scopes,plotmarks}
\usepackage{mathtools}
\usepackage{bm}
\usepackage{tensor}

%===== 背景图片
\usepackage{wallpaper}
%\URCornerWallPaper{0.1}{ecnu03s.png} % 在右上角插入背景图片

%%===== 每章生成小目录
%\usepackage{minitoc}
%\setcounter{minitocdepth}{2} % 显示到 subsection
%%\nomtcrule  % 去掉 minitoc 的横线
%\dominitoc[n] % 使 minitoc 起作用, n 表示不显示 contents 标题

%===== 参考文献与链接
% \usepackage{chapterbib} % 分章参考文献
\usepackage[numbers,sort&compress,sectionbib]{natbib}
\setlength{\bibsep}{0.5ex}
%\usepackage[xetex,pagebackref]{hyperref}
\usepackage[xetex,pagebackref]{hyperref}
\hypersetup{CJKbookmarks=true,colorlinks=true,citecolor=blue,%
	linkcolor=blue,urlcolor=blue,bookmarksnumbered=true,%
	bookmarksopen=true,bookmarksopenlevel=1,breaklinks=true}
%\renewcommand*{\backrefalt}[4]{%
%    \ifcase #1 No citations.%
%    \or Cited on page #2.%
%    \else Cited on pages #2.%
%    %\else #1 Cited on pages #2.%
%    \fi
%    }

%===== 浮动图表的标题
\usepackage[margin=2em,labelsep=period,skip=0.5em,font=normalfont]{caption}
\DeclareCaptionFormat{mycaption}%
{{\heiti\color{blue} #1}#2{\kaishu #3}}
\captionsetup{format=mycaption,tablewithin=chapter,figurewithin=chapter}

%===== 浮动对象距离设置
\usepackage{float}
\setlength{\floatsep}{10pt plus 3pt minus 2pt}
% 出现在页面顶部或底部中的浮动对象之间的竖直距离
\setlength{\textfloatsep}{10pt plus 3pt minus 2pt}
% 出现在页面顶部或底部中的浮动对象与文本之间的竖直距离
\setlength{\intextsep}{10pt plus 3pt minus 2pt}
% 出现在页面中间的浮动对象上下文之间的竖直距离

%===== 表格
\usepackage{longtable}
\usepackage{colortbl}
\usepackage{booktabs}
\usepackage{multirow,bigdelim}  % 多行
\usepackage{fancyvrb}
\fvset{formatcom=\color{blue},frame=single,rulecolor=\color{red}}

%===== 给文字加边框和背景色
%\usepackage{framed}  % shaded 环境
\definecolor{shadecolor}{gray}{0.9}
\definecolor{notecolor}{gray}{0.95}
\usepackage[framemethod=tikz]{mdframed}  % shaded 环境
\newmdenv[linecolor=green,middlelinewidth=0.5pt,%
roundcorner=3pt,backgroundcolor=yellow!5,%
innertopmargin=0.5em,innerbottommargin=0.5em,%
innerleftmargin=3pt,innerrightmargin=3pt,%
skipbelow=0.5em,skipabove=1em,%
splittopskip=\topskip]{Block}
\newmdenv[linecolor=green,middlelinewidth=0pt,%
outerlinewidth=0.5pt,
roundcorner=3pt,backgroundcolor=shadecolor,%
innerbottommargin=3pt,innerrightmargin=5pt,%
innerleftmargin=5pt,%
skipabove=0pt]{mathbox}
\newmdenv[linecolor=blue!5!green,middlelinewidth=0.3pt,%
roundcorner=3pt,backgroundcolor=red!2!white,%
% frametitle={Hello},frametitlebackgroundcolor=green!50,%
skipabove=5pt,skipbelow=2pt,%
innerleftmargin=0pt]{notebox}
\newmdenv[linewidth=0pt,roundcorner=10pt,backgroundcolor=gray!5,%
innertopmargin=1em,innerbottommargin=1em,%
innerleftmargin=2em,innerrightmargin=2em,%
skipbelow=1em,skipabove=2em,%
splittopskip=\topskip]{Quote}
\newmdenv[linecolor=red,middlelinewidth=0.5pt,%
roundcorner=3pt,backgroundcolor=white,%
innertopmargin=0em,innerbottommargin=1em,%
innerleftmargin=1ex,innerrightmargin=1ex,%
skipbelow=0.5em,skipabove=0em,%
splittopskip=\topskip]{AlgoBox}
\newenvironment{note}%
{\begin{notebox}%
		\begin{list}{\textcolor{red}{$\dag$}}{%
				\leftmargin1.8em\labelwidth1.0em\labelsep0.5em
				\itemsep0pt\itemindent0pt\parsep0pt\topsep0pt}%
			\item}
		{\end{list}\end{notebox}}
\newenvironment{think}%
{\begin{notebox}%
		\begin{list}{\raisebox{0ex}{\textcolor{red}{$\clubsuit$}}}{% \HandPencilLeft  \WhiteKnightOnWhite
				\leftmargin1.8em\labelwidth1.0em\labelsep0.5em
				\itemsep0pt\itemindent0pt\parsep0pt\topsep0pt}%
			\item}
		{\end{list}\end{notebox}}
%\newenvironment{subtit}%
%    {\begin{Block}\centering\large\hei}
%    {\end{Block}}

%===== 自定义列表
\newcounter{muni}
\newenvironment{nlist}%
{\begin{list}{{\hfill\upshape (\arabic{muni})}}%
		{\usecounter{muni}\leftmargin30pt\labelwidth24pt\labelsep.5em%
			\itemsep2pt\parsep0pt\topsep0pt\itemindent0pt}}
	{\end{list}}
\newenvironment{blist}%
{\begin{list}{{\hfill\raisebox{1.12pt}{$\bullet$}}}{%
			\leftmargin2em\labelwidth1.5em\labelsep0.5em
			\itemsep0pt\itemindent0pt\parsep0pt\topsep0pt}}
	{\end{list}}
\newcounter{exer}\numberwithin{exer}{chapter}
\newcounter{exertmp}\setcounter{exertmp}{0}
\newenvironment{exerlist}%
{%\noindent{\color{red}\rule{\textwidth}{1pt}}\par
	\begin{list}{{\hfill\color{blue}\upshape{\textit{练习}} \arabic{chapter}.\arabic{exer}}}%
		{\usecounter{exer}\setcounter{exer}{\theexertmp}%
			\leftmargin30pt\labelwidth24pt\labelsep.5em%
			\itemsep0.5em\parsep0pt\topsep0pt\itemindent0pt}}
	{\end{list}}
%    {\setcounter{exertmp}{\value{exer}}\end{list}}

%===== list
\usepackage{enumitem}
\setlist{itemsep=0.05\baselineskip,itemindent=0em,%
	partopsep=0pt,parsep=0ex,topsep=0.1\baselineskip,%
	labelwidth=1.0em,labelsep=0.5em,leftmargin=2.5em}
\setlist[enumerate,1]{label=(\arabic*), ref=(\arabic*)}
\setlist[enumerate,2]{label=\emph{\alph*}), ref=\theenumi.\emph{\alph*}}
\setlist[enumerate,3]{label=\roman*), ref=\theenumii.\roman*}

%%===== 定理环境
\usepackage[amsmath,thref,thmmarks,hyperref]{ntheorem}
\theorempreskipamount1.2em  % spacing before the environment
\theorempostskipamount0em % spacing after the environment
%\theorempostwork{\noindent}
\theoremstyle{plain}
\theoremheaderfont{\normalfont\rmfamily\bfseries\color{blue}}
\theorembodyfont{\normalfont\rmfamily\BWKai\color{black}}
\theoremindent0em
\theoremseparator{\hspace{0.2em}}
\theoremnumbering{arabic}
%\newtheorem{theorem}{\color{blue}定理}[chapter]
%\newtheorem{definition}{\color{blue}定义}[chapter]
%\newtheorem{property}[theorem]{\color{blue}性质}
%\newtheorem{lemma}{\color{blue}引理}[chapter]
%\newtheorem{corollary}{\color{blue}推论}[chapter]
%\newtheorem{remark}{\color{blue}注记}[chapter]
\colorlet{thmcolor}{green}


%\RequirePackage[most]{tcolorbox}
\definecolor{tssteelblue}{RGB}{70,130,180}
\definecolor{tsorange}{RGB}{255,138,88}
\definecolor{tsblue}{RGB}{23,74,117}
\definecolor{tsforestgreen}{RGB}{21,122,81}
\definecolor{tsyellow}{RGB}{255,185,88}
\definecolor{tsgrey}{RGB}{200,200,200}
\newenvironment{boxdefinition}
{\begin{tcolorbox}
		[enhanced jigsaw,breakable,pad at break*=1mm,
		colback=yellow!10!white,boxrule=0pt,frame hidden,
		borderline west={1.5mm}{-2mm}{tsforestgreen}]}
{\end{tcolorbox}}

\newtheorem{envdefinition}{习题}%[chapter]

\newenvironment{yyEx}
{\begin{boxdefinition}\begin{envdefinition}}
{\end{envdefinition}\end{boxdefinition}}

\newtheorem*{yySolution}{\color{blue}解:}
\newtheorem*{yySolution2}{\color{blue}另解:}
\newtheorem*{yyProof}{\color{blue}证明:}

\newenvironment{boxtheorem}
{\begin{tcolorbox}
		[enhanced jigsaw,breakable,pad at break*=1mm,
		colback=black!5,colframe=tsorange]}
	{\end{tcolorbox}}
\newtheorem{envtheorem}{定理}
\newenvironment{theorem}
{\begin{boxtheorem}\begin{envtheorem}}
		{\end{envtheorem}\end{boxtheorem}}

\newtheorem{envdef}{定义}
\newenvironment{definition}
{\begin{boxtheorem}\begin{envdef}}
		{\end{envdef}\end{boxtheorem}}

\newtheorem{envlemma}{引理}
\newenvironment{boxlemma}
{\begin{tcolorbox}
		[enhanced jigsaw,breakable,pad at break*=1mm,
		colback=tsyellow!20,boxrule=0pt,frame hidden]}
	{\end{tcolorbox}}
\newenvironment{lemma}
{\begin{boxlemma}\begin{envlemma}}
		{\end{envlemma}\end{boxlemma}}
	

%%
%%\theoremheaderfont{\normalfont\itshape\color{blue}}
%\theorembodyfont{\normalfont\rmfamily\color{black}}
%\newtheorem{example}{\color{blue}例}[chapter]

\newenvironment{proof}[1][证明]%
{\par\vspace{-2ex}\noindent\normalfont{\hei\color{blue} #1.} \upshape}
{\mbox{}\hfill\scalebox{1.2}{\ensuremath{\Box}}\medskip}
\newcommand{\mysolve}{{\upshape\hei\color{blue} 解}}

%===== 数学公式
% \setlength{\abovedisplayskip}{4pt plus1pt minus1pt}     %公式前的距离
% \setlength{\belowdisplayskip}{4pt plus1pt minus1pt}     %公式后面的距离
% \setlength{\arraycolsep}{2pt}   %在一个array中列之间的空白长度
\numberwithin{equation}{chapter}
\allowdisplaybreaks[4]
\usepackage{array}
%\usepackage{yhmath}
%\usepackage{esint} % 积分符号
%\usepackage{bbding}
%\usepackage{skak}

\usepackage[ntheorem]{empheq} % 数学公式加框和背景色
\usepackage[many]{tcolorbox}
\tcbset{highlight math %
	style={enhanced, colframe=blue!40,colback=yellow!20,arc=4pt,boxrule=1pt}}
%% Examples: equation
%\begin{equation}
%\tcbhighmath{E = mc^2}
%\end{equation}
%
%% Example: align
%\begin{empheq}[box=\tcbhighmath]{align}
%a&=b\\
%E&=mc^2 + \int_a^a x\, dx
%\end{empheq}
\newtcbox{\inlinebox}[1][]{%
	nobeforeafter, notitle, box align=center,
	fontupper=\color{blue}\bfseries, leftright skip=0.5ex,
	left=0.5mm,right=0.5mm,top=0mm,bottom=0mm,boxrule=0.8pt,
	colframe=red!80!white,colback=yellow!20!white,#1}
\newcommand{\mybox}[1]{%
	\raisebox{0.7ex}[0pt][0pt]{\inlinebox{#1}}}

%===== 算法
\usepackage{algorithm}  %\usepackage{algorithm,algorithmic}
%\usepackage[compatible]{algpseudocode}
\usepackage{algpseudocode} % algorithmicx
% algorithmicx是algorithmic的改进版，由几个子包组成，
% 包括 algpseudocode.sty, algcompatible.sty 等
\floatname{algorithm}{\color{blue} 算法}
\algrenewcommand{\algorithmiccomment}[1]{\quad{\color{red}\%\ #1}}
%\algsetup{linenosize=\small}
\numberwithin{algorithm}{chapter}
\renewcommand{\listalgorithmname}{算\ 法\ 目\ 录}
\makeatletter
\newenvironment{breakalgo}[2]{%
	\captionsetup{margin=0pt,justification=RaggedRight,singlelinecheck=false}%
	% \def\@fs@cfont{\bfseries}%
	% \let\@fs@capt\relax%
	\par\noindent%
	\begin{AlgoBox}
		\noindent\captionof{algorithm}{#1}\label{#2}%
		\vspace{-0.7\baselineskip}%
		\noindent\rule{\linewidth}{.4pt}\vspace{-0.3\baselineskip}%
	}{\end{AlgoBox}}
\newenvironment{breakalgon}{%
	\captionsetup{margin=0pt,justification=RaggedRight,singlelinecheck=false}%
	%\def\@fs@cfont{\bfseries}%
	%\let\@fs@capt\relax%
	\par\noindent%
	\medskip%
	\rule{\linewidth}{.8pt}%
	\vspace{-0.5\baselineskip}%
}{%
	\vspace{-.75\baselineskip}%
	\rule{\linewidth}{.4pt}%
	\medskip%
}
\makeatother

%===== 源代码格式
\renewcommand{\lstlistlistingname}{源代码目录}
\renewcommand{\lstlistingname}{MATLAB 源代码}
\lstset{language=Matlab}
\lstset{escapechar=`}
\lstset{basicstyle=\ttfamily\small,showstringspaces=false,tabsize=2}
\lstset{flexiblecolumns=true}
\lstset{xleftmargin=1ex,xrightmargin=1ex}
\lstset{frame=tblr,frameround=tttt}  %单线, 圆角框
%%\lstset{frame=TBLR}  %双线方框
%\lstset{frame=shadowbox,rulesepcolor=\color{blue}}
\lstset{commentstyle=\color{red},keywordstyle=\color{blue},caption=\lstname,%
	breaklines=true,backgroundcolor=\color{lightgray!20}}
%\lstset{framexleftmargin=3em,framexrightmargin=1em,framextopmargin=0.3em,framexbottommargin=0.3em}
%\lstdefinestyle{numbers}{numbers=left,stepnumber=1,numberstyle=\small,numbersep=1em}
\lstset{numbers=left, numberstyle=\small, stepnumber=1, numbersep=1em}

%\makeatletter
%\lstnewenvironment{mcode}[1][]
%  {\lstset{language=Matlab,basicstyle=\small\ttfamily,
%    numbers=none,nolol,title=\textcolor{blue}{\textsf{MATLAB}},frameround=tttt,
%    backgroundcolor=\color{lightgray!20},rulecolor=\color{blue!5!green},%
%    xleftmargin=0.5em,xrightmargin=0.5em,#1}%
%    \csname\@lst @SetFirstNumber\endcsname}
%    {\csname\@lst @SaveFirstNumber\endcsname}
%\makeatother
%\newcommand{\emcode}{\addtocounter{lstlisting}{-1}}

%===== 页眉和页脚
\pagestyle{fancy}
\fancyhf{}  %清除以前对页眉页脚的设置
% 定义页眉与正文间双隔线
%\newcommand{\makeheadrule}{%
%    \makebox[0pt][l]{\rule[.7\baselineskip]{\headwidth}{0.5pt}}%
%    \rule[0.85\baselineskip]{\headwidth}{0.8pt}\vskip-.8\baselineskip
%    }
%\makeatletter
%\renewcommand{\headrule}{%
%    {\if@fancyplain\let\headrulewidth\plainheadrulewidth\fi
%     \makeheadrule}}
%\makeatother
% 画单隔线
%\renewcommand{\headrulewidth}{0.5pt} % 页眉下面的分隔线
%\renewcommand{\footrulewidth}{0pt}   % 页脚上面的分隔线
\renewcommand{\chaptermark}[1]{\markboth{\CTEXthechapter\ \ #1}{}} % 章标题
\fancyhead[RE]{\leftmark}
\renewcommand{\sectionmark}[1]{\markright{\thesection\ \ #1}{}} % 节标题
\fancyhead[LO]{\rightmark}
\fancyhead[RO,LE]{$\cdot$\ \thepage\ $\cdot$}

%===== 习题解答
\usepackage{answers}
\Newassociation{sol}{Solution}{ans}
\newenvironment{nproof}[1][证明]% 习题解答专用
{\par\noindent\normalfont{\hei\color{blue} #1.} \color{blue}\kaishu\upshape}
{\mbox{}\hfill\scalebox{1.2}{\ensuremath{\Box}}\medskip}

%===== 自定义命令
\renewcommand{\C}{\mathbb{C}}
\newcommand{\Cm}{\mathbb{C}^{m\times m}}
\newcommand{\Cn}{\mathbb{C}^{n\times n}}
\newcommand{\Cnm}{\mathbb{C}^{n\times m}}
\newcommand{\Cmn}{\mathbb{C}^{m\times n}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\Rm}{\mathbb{R}^{m\times m}}
\newcommand{\Rn}{\mathbb{R}^{n\times n}}
\newcommand{\Rmn}{\mathbb{R}^{m\times n}}
\newcommand{\Xbb}{\mathbb{X}}
\newcommand{\Pbb}{\mathbb{P}}
\newcommand{\Zbb}{\mathbb{Z}}
\newcommand{\Vbb}{{\mathbb{V}}}
\newcommand{\Wbb}{{\mathbb{W}}}
\newcommand{\Lbb}{{\mathbb{L}}}
%
\newcommand{\A}{\mathcal{A}}
\renewcommand{\H}{\mathcal{H}}
\newcommand{\K}{\mathcal{K}}
\renewcommand{\L}{\mathcal{L}}
\renewcommand{\O}{\mathcal{O}}
%\newcommand{\DD}{\mathcal{D}}
\newcommand{\FF}{\mathcal{F}}
\newcommand{\PP}{\mathcal{P}} % 集合
\newcommand{\QQ}{\mathcal{Q}} % 集合
\renewcommand{\SS}{\mathcal{S}} % 集合, 子空间
\newcommand{\WW}{\mathcal{W}} % 集合, 子空间
\newcommand{\TT}{\mathcal{T}} % 集合
\newcommand{\ZZ}{\mathcal{Z}} % 集合
\newcommand{\ZZn}{\mathcal{Z}^{n\times n}} % Z-矩阵集合

\newcommand{\II}{\mathrm{\bf I}} % 不变算子
\newcommand{\EE}{\mathrm{\bf E}} % 位移算子
%
\renewcommand{\Re}{\mathrm{Re}}
\renewcommand{\Im}{\mathrm{Im}}
\newcommand{\ii}{\bm{\mathrm{i}\,}}
\newcommand{\Ran}{\mathrm{Ran}}
\newcommand{\Ker}{\mathrm{Ker}}
\newcommand{\ddiv}{\mathrm{div}}
\newcommand{\gap}{\mathrm{gap}}
\newcommand{\vvec}{\mathrm{vec}}
%\newcommand{\myvec}[1]{\mathrm{\textbf{#1}}}
\newcommand{\rr}{\bm{\mathrm{r}}}  % Numerical Radius
\newcommand{\Co}{\mathrm{Co}}
\newcommand{\TV}{\mathrm{TV}}
\newcommand{\Toep}{\bm{\textsf{T}}}
\newcommand{\Hankel}{\bm{\textsf{H}}}
\newcommand{\Circ}{\bm{\textsf{C}}}
\newcommand{\LDLT}{\ensuremath{\mathrm{LDL}^\T}}
\newcommand\opt{{\rm opt}}
%
\newcommand{\lam}{\lambda}
\newcommand{\Lam}{\Lambda}
\newcommand{\eps}{\varepsilon}
\newcommand{\xt}{{x_*}}
\newcommand{\yt}{{y_*}}
%\newcommand{\T}{\intercal}
%\newcommand{\T}{{\raisebox{1pt}[0pt]{\scriptsize$\intercal$}}}
\renewcommand{\d}{\mspace{4mu}\mathrm{d}}
\newcommand{\p}{\partial}
\newcommand{\grad}{\nabla}
\newcommand{\adots}{\reflectbox{$\ddots$}}
\newcommand{\ie}{\emph{i.e.}}
%
\newcommand{\beq}{\begin{equation}}
\newcommand{\eeq}{\end{equation}}
\newcommand{\bbm}{\begin{bmatrix}}
	\newcommand{\ebm}{\end{bmatrix}}
\newcommand{\ol}[1]{\overline{#1}}
\newcommand{\wt}[1]{\widetilde{#1}}
\newcommand{\Cond}{\kappa}
%
\newcommand{\dis}{\displaystyle}
\newcommand{\code}[1]{\textcolor{blue}{\ttfamily #1}}
\newcommand{\function}[1]{\textcolor{blue}{\bfseries #1}}
\newcommand{\ip}[1]{\ensuremath{( #1 )}}
\newcommand{\mycite}[1]{{\upshape\cite{#1}}}
\newcommand{\myind}[1]{{\hei\upshape\color{blue} #1 }\index{#1}}
\newcommand{\myindd}[2]{{\hei\upshape\color{blue} #1}\index{#2}}
\newcommand{\mydef}{\triangleq}
\newcommand{\mycolon}{\!:\!}
\newcommand{\mymid}{\,:\,}
\newcommand{\myss}{\scriptstyle}
\newcommand{\ssrm}[1]{{\scriptscriptstyle\mathrm{#1}}}
\newcommand{\myem}[1]{{\hei\upshape\textcolor{blue}{#1}}}
\newcommand{\myif}[2]{\textbf{if} #1 \textbf{then} #2}
\newcommand{\rA}{r_{\scriptscriptstyle\! A}}
\newcommand{\lev}{\textit{lev}}
\newcommand{\bslx}{\hfill{\upshape\color{blue}(留作练习)}}
%
\DeclareMathOperator{\sspan}{span}
\DeclareMathOperator{\ddim}{dim}
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator{\tridiag}{tridiag}
\DeclareMathOperator{\mvec}{vec}
\DeclareMathOperator{\rank}{rank}
\DeclareMathOperator{\sign}{sign}
\DeclareMathOperator{\fl}{fl}
\DeclareMathOperator{\der}{D} % 导数算子
\DeclareMathOperator*{\argmin}{argmin}
\DeclareMathOperator{\tr}{tr}
\newcommand{\MATLAB}{MATLAB}
%
\DeclareMathAlphabet{\mathsfsl}{OT1}{cmss}{m}{n}
\SetMathAlphabet{\mathsfsl}{bold}{OT1}{cmss}{bx}{n}
\newcommand{\DD}{\mathsfsl{D}}
%
\newcommand{\tbc}{\textcolor{blue}{\it To be continued ... }\bigskip}
%
\renewcommand{\baselinestretch}{1.3}



\begin{document}

\frontmatter
\begin{titlepage}\Large
\renewcommand{\thefootnote}{\fnsymbol{footnote}}
  \pdfbookmark[0]{封面}{Cover}
  \begin{center}
  \vspace*{3cm}
  {\hei\Huge 工程数学学习指南} \bigskip

  {\hei\LARGE 杨~~勇~~编著} \medskip

  \today

  \end{center}
\end{titlepage}




\clearpage{\pagestyle{empty}}
\vspace*{0.04\textheight}
\begin{center}\Large\
	\textbf{
		前~~言\bigskip
	}
\end{center}


本书是《工程数学: 复变函数、矢量分析与场论、数学物理方法》一书的课后习题题解. 郭玉翠教授的这本书继承了许多位北京邮电大学数学系教授的教学经验，但是令人遗憾的是此书的习题却一直没有一份答案可供参考. 而作者写本书的目的是在这里给大家提供帮助, 力求使这门课不那么难学.

文学家王蒙曾说过: 最高的数学和最高的诗一样, 都充满了理想, 充满了智慧, 充满了创造, 充满了章法, 充满了和谐也充满了挑战. 诗和数学又都充满了灵感, 充满了激情, 充满了人类的精神力量. 那些从诗中体验到数学的诗人是好诗人, 那些从数学中体会到诗意的人是好数学家. 最高的诗是数学, 这是文学家对数学的推崇. 亲爱的同学们, 诗言志, 希望你们能从这里读出诗的理想, 接受诗的智慧, 学会诗的创造, 掌握诗的章法, 体验诗的和谐, 勇敢地迎接未来的挑战.

基础数学分为代数、几何、分析三大类. 而工程数学则是一门应用数学, 同学们在前面的学习中惟独没有这种应用数学. 初次走进数学物理方法, 第一个感觉是难, 这个感觉恰如第一次接触“诗经”的“风、雅、颂”一样. 不要怕难, 这是诗意的挑战. 在学习这门课的过程中, 抽象概念会变得形象直观, 给我们打下深刻的烙印. 通过严格的逻辑推理和抽象思维的训练, 这些基础知识将融化在你的血液中. 你会感觉数学和诗一样, 充满了灵感, 充满了激情, 充满了人类的精神力量, 你的数学生涯也就化为诗样的人生.

郭玉翠教授这本书的习题是多了一些, 这也要请同学们根据自己的情况适当地选择, 不必题题都做; 更不要因为有几个题做不出来而失去信心. 对作者而言, 一题之解, 有时也累日始成, 可以说不时就遇到了不小的困难, 倾注了不少心力. 对读者而言, 作者切望本书是备而不用、备而少用. 有能力的同学应当尝试独立完成每一道习题. 如碰到一个题一时做不出来, 宁肯暂时搁一搁, 也不要轻易翻看本解答. 譬如登山, 经过艰苦努力上了峰顶, 自有其乐趣和成就感. 反之, 如在未尽全力之前就任人抬上去,则不惟无益, 实足以挫折信心.

尽管做了不少努力以使读者学习本课程会比较容易些, 但是, 理解这样的课程内容并获得灵活使用它解决具体问题的能力是个复杂的过程. 这门课程的难度相比数学分析会呈现出一个飞跃. 初学者不能指望这个过程会在完全不遇到困难的情况下轻松地通过. 大家会遇到许多与前不同的、大大小小的困境, 这是完全可以理解的, 在一定意义上来说也是正常的. 具有强烈求知欲的学而不厌者方能成功地完成这个困难的过程.如果读者在阅读本书时遇到了困难, 可与作者联系, 电子邮件:\url{Yang945841548@bupt.edu.cn}

龚政同学仔细审阅了本书初稿, 并对第九章的部分推导提供了很好的修改意见, 特致谢意. 作者在参考了这些意见的基础上, 对该章的初稿进行了修改, 使得该章的质量有了很大的提高. 作者还要感谢母校的同学们给予的支持和帮助.

囿于作者的水平和经验, 书中不妥以至谬误之处, 在所难免. 尚祈同学们不吝指教. 最后, 赠送一句话与大家共勉:
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	{\BWKai\color{blue}
		纸上得来终觉浅，绝知此事要躬行。\bigskip
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	{\kaishu{~~杨~~勇~~~~~~~~~~~}}
	
	2019年 9 月于北京昌平
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